Optimization of Doping CdTe with Group-V Elements: A First-Principles Study

Group-V substitution at the $\mathrm{Te}$ site, ${X}_{\mathrm{Te}}$ (X = $\mathrm{P}$, $\mathrm{As}$, $\mathrm{Sb}$), under $\mathrm{Cd}$-rich conditions is an effective way to enhance the hole density and, in the meantime, suppresses the dominant nonradiative carrier recombination center in $\mathrm{Cd}\mathrm{Te}$, thus, improving the performance of $\mathrm{Cd}\mathrm{Te}$ thin-film solar cells. However, it is not clear which group-V dopant, X, is the most effective dopant, because it is expected that ${\mathrm{P}}_{\mathrm{Te}}$ will have the shallowest acceptor level due to its high electronegativity, whereas ${\mathrm{Sb}}_{\mathrm{Te}}$ will have the smallest formation energy due to its small size mismatch with $\mathrm{Te}$. Our systematic first-principles study shows that the hole concentration contributed by the acceptor ${X}_{\mathrm{Te}}^{\ensuremath{-}}$ is limited by the related compensating $A{X}^{+}$ center that increases simultaneously with ${X}_{\mathrm{Te}}^{\ensuremath{-}}$ as the chemical potential of dopant X increases. However, the ratio of ${X}_{\mathrm{Te}}^{\ensuremath{-}}$ acceptors to the $A{X}^{+}$ donors can be significantly increased if the sample is grown at high temperature and then annealed to room temperature, achieving a high hole density and low Fermi level $({E}_{F})$. We find that all group-V ($\mathrm{P}$, $\mathrm{As}$, and $\mathrm{Sb}$) dopings can achieve maximum hole densities of about ${10}^{17}\phantom{\rule{0.25em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, which are consistent with previous experimental results. Despite the relatively deep acceptor level of 150 meV, $\mathrm{Sb}$ doping can achieve a considerable hole density due to the low formation energy of substituting $\mathrm{Sb}$ for $\mathrm{Te}$ with similar atomic radii. $\mathrm{P}$ doping can achieve a higher hole density than that of $\mathrm{Sb}$ due to its shallow transition energy at \ensuremath{\epsilon}(0/\ensuremath{-}) = 70 meV. However, the highest hole density is achieved through $\mathrm{As}$ doping, which is attributed to its balanced defect level at \ensuremath{\epsilon}(0/\ensuremath{-}) = 80 meV and relatively small formation energy.